Kerimov sold Anzhi past year.
Kerimov was arrested at Nice airport overnight into Tuesday.
The judge decided that Kerimov could be released from detenion but had to turn in his passport and could not leave the Alpes-Maritime county Nice is in.
"We will apply all efforts, maximum of efforts, to defend his legal interests", a Kremlin spokesman said.
The source added Kerimov would be held in custody for at least another 24 hours.
Moscow is taking "all necessary steps" to protect Russian upper house lawmaker Suleiman Kerimov and will continue to do so, Kremlin spokesman Dmitry Peskov said, adding that the Senator is also "protecting his interests himself".
Kerimov is ranked by Forbes magazine as Russia's 21st wealthiest businessman, with a net worth of $6.3 billion.
Shares in Polyus fell more than 3 percent in early trade in Moscow on Wednesday but then recovered some ground to close down 1.25 percent.
Kerimov, 51, one of Russia's richest men, was arrested late on Monday night in Nice, southern France and then released under strict conditions, the BBC reported.
Kerimov shot to fame in the soccer world in 2011 when he bought Russian club Anzhi Makhachkala and went on a spectacular spending spree.
A French judicial source said Kerimov faces accusations of purchasing several luxury homes on the French Riviera using shell companies, which would have enabled him to reduce his tax obligations to France.